Wednesday, January 9, 2008

Physics: No Infinities

I studied physics for three and a half years at university, just long enough to understand the stuff.

Unfortunately, I have found that, like most people, scientists are bad at logic-fu. Really bad.

This would obviously come as a shock to most scientists, and they would scoff. After all, supposedly their reasoning abilities are vital for their job.

To demonstrate my point of view, I would like to propose a new fundamental law of physics, on par with conservation of mass or Newton's Third.

The No Infinities PrincipleThe Principle states that anything that requires an infinity doesn't exist.

Said differently, it means that whenever a mathematical model of the universe goes to infinity, or can be rearranged to go to infinity, that equation is wrong.

Why does this demonstrate that scientists suck at thinking? Because it's completely obvious. To a physicist, an infinity always represents a mistake. They don't talk about it in class, and I suspect they don't talk about it at conferences either, but an infinity in the equations doesn't mean that a physical quantity is going to infinity. It means the equation has broken. Everyone just assumes this is true, and works accordingly - as it turns out, with unintentional good reason.

For instance, a physicist can say, "When does a neutron decay? At infinity." This is equivalent to saying, "Never." Similarly the place where parallel lines meet. When we say that a black hole's density is infinity, we mean that we have no fucking clue what's going on in there. Also, there are many different types of coordinate systems one can use to describe space, but some of them go to infinity at various points - and even if they perfectly describe the physics everywhere else, it means that at these points, it's wrong.

And yet...and yet...occasionally, physicists forget this.

For instance, the idea of an eternal universe is respectable. However, it can be debunked like so:

Assume time is infinite. Since time is relative, we can designate now as t=0.

Let us perform a transformation to go infinitely far in the past. In an eternal universe, this is possible.

Therefore, we are now at t=0-infinity=-infinity

There is a problem. There is no transformation that we can perform to get back to the present. t=infinity-infinity is undefined. In other words, the present is undefined in terms of the past.

For the layman, this means that any equation that describes the past cannot also describe the present, and vice-versa, because to find the relationship between two points in time, you have to perform a transformation.

Also, because the time t=0 is arbitrary, this is true for all points in time.

If time is infinite, time is undefined.

Which, given the nature of the No Infinities Principle, is exactly what you would expect. Infinite quantities are undefined.

Indeed, with infinite time, one would naturally expect that time would become meaningless. Any finite quantity would be swallowed up infinitely far before the present, and only time-independent phenomena would remain.

Additionally, the idea of an infinite universe - one that goes on forever in space - is also palatable. In fact, it is nonsense. In an infinite universe, there would be infinite matter. Therefore, there would be infinite energy, and small perturbations in the energy would be allowed.

Mathematically:

Energy=E_1=infinity.

Let's violate conservation of energy!

E_2=infinity+10,000,000GJ.E_2=infinity=E_1

According to the math, we haven't actually violated conservation of energy. Therefore, in an infinite universe, conservation of energy would also be meaningless. I suspect space itself would be meaningless as well, pretty much exactly the way time would be, but can't as yet prove this.

There is, of course, the De Sitter horizon. Everything is accelerating away from us, it appears, which means that there is an event horizon in the cosmos. This is because of complicated General Relativity conclusions that I don't actually understand well. But basically, everything further away than the De Sitter horizon is accelerating so fast that light will never manage to cross the entire distance from it to us.

There is a small problem with the De Sitter horizon. The cosmos are expanding, but it's staying put. Energy can disappear behind it forever. This violates the law of conservation of energy. But, I hear you say, it's not really destroyed, is it? We just can't reach it anymore?

Ah ha! We can't tell the difference. We learned from Einstein's relativity that something that appears, for instance, foreshortened, is actually physicallyforeshortened, whatever it's 'rest length' is supposed to be.

If energy is disappearing forever, it's actually disappearing forever - being destroyed. It doesn't matter how or why, or even if it secretly still exists. Even black holes obey conservation of energy. Physics would collapse without it.

In fact we learn from physics in general that whenever two things appear to be the same, they are the same. There's no secret hidden variable that make things actually different.

For instance, we worked out the mathematical description for waves in water, and in air and so on. Later, I can't remember if it was Maxwell himself or if Einstein did it first, but we found the exact same equation when we combined Maxwell's equations in a specific way.

The problem is, we knew that waves in water were just an aggregate, emergent phenomenon. In reality there's no such thing as a water wave, just a bunch of water atoms moving in circles.

However, we quickly found that there doesn't appear to be anything for electromagnetism to wave around. It seems that it's a wave...of waves. Just sort of a wave in itself.

Nevertheless, the math is the same. They look the same, therefore, they are the same. A wave is a wave is a wave, even if we don't really know what a wave is.

So clearly, because modifying conservation of energy would literally bring physics to its knees, and we haven't had to bring physics to its knees to describe most of the universe, we can assume that if we can construct a system that violates conservation of energy, that system does not exist.

I can hear the distance rustlings of counter-arguments on this point, so while I can't definitively prove it, I find it very hard to believe that one such system is the whole physical universe.

That was rather longer than I intended, but there you go. Things look like what they are, and the universe can't be infinite.

I've now demonstrated two very obvious conclusion from the No Infinities Principle. This is a principle widely accepted by physicists, and yet no one, as far as I know, has brought up the fact that it means time and space are finite. Thus, we can conclude that they're fucked in the head, and also that the principle is sound.

Like conservation of energy and Newton's Third, the No Infinities Principle often manifests in surprising ways, almost like magic. At first glance, it seems like various conserved energies and various conspicuously missing infinities have little in common. It seems like all the proofs that it must be so are quite different and individual.

Yet, each time, you can predict with certainty that conservation of energy isn't being violated, but perhaps stealthed, without having to go through the tedious business of proving it. I submit that the same is true for infinities. Any physically relevant infinity that you can construct mustnot exist. It will always be so, but not necessarily obvious.

My first prediction is that black holes cannot exist. While clearly, something very similar exists, black holes as such cannot, because singularities are impossible.

However, anyone who's actually qualified in physics will find this unimpressive. I'm hardly the first to predict this.

However, there is a similar phenomenon that I haven't seen connected. I hope, for the sake of physicists, that they simply don't feel the need to mention this to undergrads. It would be very embarrassing for them if I am actually the first to formalize this.

Electrons also don't exist. They are point-like particles, in other words infinitely small. Also, their charge density is infinite, and the electric field at their core is infinite.

If you are a student of physics you will notice, dear reader, that the electron never, ever acts like a point particle. It is shielded by the uncertainty principle. Because the electron's position is smeared out over space, it's origin is similarly smeared out. The field will never actually go infinite, the charge density isn't ever actually infinite.

Two separate phenomena. Entirely different - one an aggregate formed from gravitational interactions, the other a fundamental particle with an electric nature.

One is shielded by an event horizon which, while theoretically things are happening behind, we can never cross, the other protected by a fundamental property of quantum mechanics. (Also, waves in general, incidentally.)

Both, however, preventing actual physical infinities. Hmm. Hmm!

I will mention one other prediction. Space must be quantized, because otherwise infinitely small distances can exist. While there's some speculation already that space may be quantized, by the No Infinities Principle it cannot be otherwise. In this case, it appears that a particle with enough energy, and thus a small enough wavelength, to probe below the Planck Scale becomes a black hole and swallows itself.

Elsewhere I will prove that the No Infinities Principle is equivalent to causality, which is equivalent to the fact that the universe is describable using math. If so, then A: there's no chance in hell I'm wrong and B: physicists really had their thumb up their butts not to formalize this before I did.

While I haven't studied other fields as comprehensively as physics, as I don't consider them as important to philosophy, it appears that their doctorate-holders are as gormless as the physicists.

Indeed, it's quite clear that not one single university course in existence teaches the ability to think. Quite a few may pretend to, but not one does. Given this environment, it is unsurprising that while professors are certainly intelligent and knowledgeable, they are horrendous thinkers.

Still, I usually welcome being wrong. Finding that I was wrong almost guarantees that I just became right, after all. If there are non-stupid objections to the No Infinities Principle, I will hopefully welcome them.

But frankly, my only real concern is that someone may have thought of it before me. However, I had to personally prove that time and space are finite. I find this reassuring.

Not for science, sadly. Our science is moribund. For philosophy. Battered and beaten, nearly stillborn, philosophy may finally be raising its head out of the mud.

3 comments:

Interesting. I agree with you that an infinity in physics tells us our parameters are not quite correct, but these theories have survived all tests to refute them, so the infinity within physics is not a problem for the time being - in fact it is a minor quibble. Furthermore, infinities do exist - in mathematics.